Swelling following a stroke is very common, especially in the upper limbs. But it's important to do some investigation before you start addressing the problem.
First, find out if something unrelated to the stroke is causing the problem. Could your mother have injured her hand in some way? People tend to lose sensation when they have a stroke, so she may have inadvertently banged it.
If that's not the cause, have your mother's doctor make sure she doesn't have a deep vein thrombosis (DVT) in her arm. A DVT is a blood clot that forms in a vein deep in the body. Her doctor needs to rule it out because many of the things that might be done to help normal swelling could send the clot to the lungs.
If the swelling isn't the result of an injury or a blood clot, it's most likely a dependent edema brought about by weakness in her arm. When the hand's normal muscle pumping is disrupted by disuse (in this case, because of the stroke), fluid begins to pool in the tissues along the back of the hand and in the forearm. So the fluid needs to be pushed back into her bloodstream.
But there's another catch: Pushing the fluid out of your mother's hand and arm will increase her blood volume. If she has any cardiac problems, her heart might not be able to handle the increased load. So it's very important that your mother see her doctor before you do anything.
Once the doctor gives you the okay, the first thing to try may be elevating your mother's hand. If you prop her arm on pillows above the level of her heart, gravity will help move the fluid back into circulation.
Pumping exercises for the hand will also help move fluid back into the bloodstream. Have your mother close her hand tightly and open it, 10 to 20 times in a row. She can do this several times a day.
Compression garments and wraps can also be used to gently push the fluid back into circulation. You can buy garments and wraps through an occupational therapist's office, but you could also try Isotoner gloves, available in some department stores, to give your mother's hand some good compression. Use the glove for the opposite hand, turned inside out, so that the seams won't dig into the swollen area.